Welcome to the next talk related to Webinar DISA-DSM: stochastic analysis, statistics and machine learning, which is held by Huyên Pham (University Paris 7 Diderot, France)
When? 3 November at 13:00 Stockholm time.
Online via zoom: Contact Nacira Agram, firstname.lastname@example.org, to get the link
Title: Solving mean-field PDE with symmetric neural networks
Abstract: We propose numerical methods for solving non-linear partial differential equations (PDEs) in the Wasserstein space of probability measures, which arise notably in the optimal control of McKean-Vlasov dynamics.
The method relies first on the approximation of the PDE in infinite dimension by a backward stochastic differential equation (BSDE) with a forward system of N interacting particles. We provide the rate of convergence of this finite-dimensional approximation for the solution to the PDE and its Lions-derivative. Next, by exploiting the symmetry of the particles system, we design a machine learning algorithm based on certain types of neural networks, named PointNet and DeepSet, for computing simultaneously the pair solution to the BSDE by backward induction through sequential minimization of loss functions. We illustrate the efficiency of the PointNet/DeepSet networks compared to classical feedforward ones, and provide some numerical results of our algorithm for the examples of a mean-field systemic risk and a mean-variance problem.
Based on joint work with M. Germain (LPSM, EDF) and X Warin (EDF).
We will book a room at LNU for those who wants to attend physically the seminar. Because of space restrictions due to Covid-19, please let me know if you want to do that.
A warm welcome!